Limited permeable crack moving along the interface of a piezoelectric bi-material

• Published in: European journal of mechanics, A, Solids Vol. 30; no. 5; pp. 639 - 649
• Main Authors: Lapusta, Y., Komarov, A., Labesse-Jied, F., Moutou Pitti, R., Loboda, V.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Masson SAS 01-09-2011; Elsevier
• Subjects: Civil Engineering; Construction durable; Electric flux; Electric traction; Engineering Sciences; Exact sciences and technology; Exact solutions; Fracture mechanics; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Limited permeable conditions; Materials; Mathematical analysis; Mathematical models; Matériaux composites et construction; Moving crack; Physics; Piezoelectric materials; Piezoelectricity; Solid mechanics; Structural and continuum mechanics; Structures; Subsonic speed; Traction; Limited permeable conditions; Moving crack; Piezoelectric materials; Electric traction; Crack array; Energy release; Mode coupling; Riemann problem; Solid solid interface; Rupture; Moving boundary; Permeability; Coordinate system; Homogeneous material; Modeling; Crack propagation; Exact solution; Stress intensity factor; Hilbert problem; Piezoelectricity; Crack tip; Interface crack; Asymptotic approximation; Electromechanical properties
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2011.04.005

A plane problem for a crack moving with a subsonic speed along the interface of two piezoelectric semi-infinite spaces is considered. The crack is assumed to be free from mechanical loading. The limited permeable electric condition with an account of electric traction is adopted at its faces. A uniformly distributed mixed mode mechanical loading and an electric flux are prescribed at infinity. The problem is reduced to the Riemann–Hilbert problem by means of introducing a moving coordinate system and assuming that the electric flux is uniformly distributed along the crack region. An exact solution of this problem is proposed. It permits to find in closed form all necessary electromechanical characteristics at the interface and to formulate the equation for the determination of the electric flux. Analysis of this equation confirms the correctness of the assumption concerning the uniform distribution of the electric flux in the crack region. The values of the electric flux are determined by solving the obtained equation. Thereafter, the stress and electric intensity factors as well as their asymptotic fields at the crack tip are also found. The particular case of a crack moving in a homogeneous piezoelectric material is considered. The values of the electric flux and the fracture parameters are found exactly in a simple form for this case. Also, a numerical analysis is performed for a crack propagating with a subsonic speed between PZT4 and PZT5 materials and for a crack moving in PZT4 material. The electric flux in the crack region, stress and electric intensity factors, crack opening and the energy release rate (ERR) are found as functions of the crack speed, loading and electric permeability of the crack medium. The influence of the electric traction on the crack faces upon the mentioned parameters is demonstrated.